Three 1.0 - flasks, maintained at 308 K , are connected to each other with stopcocks. Initially,

step 1 So to begin this problem, let's start off with what we know. So we have three flasks. One of the

Three 1.0 - flasks, maintained at 308 K , are connected to...

Three 1.0 - flasks, maintained at 308 $\mathrm{K}$ , are connected to each other with stopcocks. Initially, the stopcocks are closed. One of the flasks contains 1.0 atm of $\mathrm{N}_{2} ;$ the second, 2.0 $\mathrm{g}$ of $\mathrm{H}_{2} \mathrm{O} ;$ and the third, 0.50 $\mathrm{g}$ of ethanol, $\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}$ . The vapor pressure of $\mathrm{H}_{2} \mathrm{O}$ at 308 $\mathrm{K}$ is 42 $\mathrm{mm} \mathrm{Hg}$ and that of ethanol is 102 $\mathrm{mmHg.The~stop-}$ cocks are then opened and the contents mix freely. What is the pressure?

Key Concepts

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, relates the pressure, volume, and temperature of a gas to the number of moles present. It is crucial for calculating the behavior of gases under different conditions and is often used to determine the number of moles in a system when pressure and temperature are known.

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of gases, the total pressure is equal to the sum of the partial pressures of each individual gas. This concept allows us to analyze mixtures by considering the contribution of each gas separately, assuming they do not interact chemically.

Vapor Pressure and Phase Equilibrium

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. In a closed system, once equilibrium is reached, the vapor pressure remains constant regardless of the amount of liquid present, highlighting the concept of phase equilibrium between the gaseous and condensed phases.

Transcript

00:01 So to begin this problem, let's start off with what we know.

00:03 So we have three flasks.

00:05 One of them has one atmospheres of nitrogen.

00:08 The second one has two grams of water.

00:11 And the third one has 0 .5 grams of ethanol.

00:15 And we are given that the vapor pressure of ethanol, sorry of water, is 42 millimeters mercury.

00:26 And the vapor pressure of ethanol is 102 millimeters mercury.

00:41 So we want to find the pressure of all of these three flasks if they were combined together.

00:51 So to begin, we must first know that what we're looking for here is the total pressure.

01:00 And total pressure is the amount of pressure created by all substances within one container.

01:08 In our case, since all of these three flasks are connected together, our total volume will be three liters because each of these flasks are one liter each.

01:28 So to reach the total pressure, we're going to have to just add all of these, the pressures of these combined substances.

01:36 It would be the pressure of nitrogen plus the pressure of water, plus the pressure of ethanol.

01:48 So let's first start off with finding the pressure of nitrogen, which we conveniently already have.

01:59 We know that in its own flask, it is one atmosphere for one liter.

02:11 But how do we know the pressure for when it's released into the rest of the flasks? so when it's 3 liters.

02:22 Well, we can solve this using boyle's law, which is p1 v1 equals p2 v2.

02:33 Using what we know, we can just plug in numbers and find the pressure.

02:38 So let us rearrange this equation to solve for what we know, so for what we don't know, rather.

02:51 And this will be one atmosphere times one liter, and we're looking for the pressure for three liters.

03:05 And that gives us 0 .33 atmospheres.

03:12 So we know nitrogen's partial pressure will be 0 .33 atmospheres.

03:22 So now for the next one, we're looking for the pressure of water.

03:32 And we're only given the mass.

03:34 We see that we only have two grams of water.

03:37 We're going to have to find the pressure from this.

03:41 And the first logical step is to find the amount of moles.

03:47 So we start off with two grams.

03:50 The first thing we can do is divided by the molar mass.

03:54 That's the easiest way to get moles.

03:59 And so we do some dimensional analysis because we know the molar mass of water is 18 .02 grams per mole.

04:07 So we take our two grams and multiply it by one mole divided by 15 .02 grams, cross out like values, like units.

04:20 And we get .11 moles.

04:24 So now we have moles.

04:26 And since we're dealing with gas here, we can find the pressure using the ideal gas law, which is pv equals n, wrong n.

04:40 N.

04:40 N .t.

04:43 So we have the temperature, which is 308 kelvin.

04:46 We have the moles, which we got right now.

04:48 We have the volume, and we have the pressure.

04:52 Now we just plug in, or we can rearrange first.

04:56 That would be helpful.

04:56 So we rearrange to find the pressure.

05:01 Now, keep in mind that it is only going to be, it will be three liters.

05:10 Keep in mind that it's going to be three liters because we're solving for the pressure together rather than in the individual flask...

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